Abstract: A method reduces the structure factor phase ambiguity corresponding to a selected reciprocal lattice vector. The method includes generating an original phase probability distribution corresponding to a selected structure factor phase of the selected reciprocal lattice vector. The original phase probability distribution includes a first structure factor phase ambiguity. The method further includes combining the original phase probability distribution with a plurality of phase probability distributions of a plurality of structure factor phases of other reciprocal lattice vectors using a phase equation or inequality. The phase equation or inequality defines a mathematical relationship between the selected structure factor phase of the selected reciprocal lattice vector and the plurality of structure factor phases of other reciprocal lattice vectors. The method further includes producing a resultant phase probability distribution for the selected structure factor phase of the selected reciprocal lattice vector.

Abstract: A method uses linear prediction analysis to define a first structure factor component for a first reflection from x-ray crystallography data. The x-ray crystallography data includes a set of cognizable reflections. The method includes expressing the first structure factor component as a first linear equation in which the first structure factor component is equal to a sum of a first plurality of terms. Each term includes a product of (1) a structure factor component for a cognizable reflection from the x-ray crystallography data, wherein the cognizable reflection has a separation in reciprocal space from the first reflection, and (2) a linear prediction coefficient corresponding to the separation between the cognizable reflection and the first reflection. The method further includes calculating values for the linear prediction coefficients.